Solve the heat equation PDE using the Implicit method in Python

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@leolasagne9418 2 жыл бұрын

very nice, thank you! But isn't that the Implicit euler and not the crank-nicolson? en.wikipedia.org/wiki/Finite_difference_method

@shameelabdulla1491 2 жыл бұрын

Thanks for pointing this out. Yes you are correct. I'll try to make the correction in my video. I'll work on the actual Crank Nicholson method at a later stage and post it.

@indribelu 2 жыл бұрын

@@shameelabdulla1491 Sir, has the video about the Nicolson Crank Meode been uploaded? I'm really waiting for your video, it's very useful and I really need to learn about it sir. Thank you

@indribelu 2 жыл бұрын

@Leo Lasagne sir, can you recommend a video about the nicolson crank method? I really need that. Thank you

@leolasagne9418 2 жыл бұрын

@@indribelu sorry, sadly I don't know a Video.

@peterthomson1753 Жыл бұрын

@@indribelu I assume you don't need this anymore, but the process fro Crank-Nickolson would be almost the same apart from the integrator solver being slightly different. You could probably google for notes on the crank nicholson solver and try changing the code yourself, this would be a great way to learn how to implement this for yourself.

@peterthomson1753 Жыл бұрын

This is a great video. It makes the solution feel so simple, when my lecturers sometimes make it feel so hard. This will help me so much for my computational sciences revision and learning how to actually implement these solutions. Thank you!

@ngdnhtien Жыл бұрын

For those who wonder, if one were to change the space discretization condition (dx), which would result in more (or less) grid points, simply change the multiplying factor of number of diagonal elements to, in this case, (T.shape[0]-2)*[1+2*factor] for axis 0; and sub-diagonal elements to (T.shape[0]-3)*[1+2*factor] for axis -1 and +1 when generating the A matrix. And thanks Shameel for the great video. The .copy() explanation was excellent. Was working on another problem the other day and messed up everything having no clues what was going on; now I realize it was me naively managing memory slots.

@wajahathussain2688 2 жыл бұрын

good job, but if the x range is 0 to 2 how we define boundary condition at 2

@shameelabdulla1491 2 жыл бұрын

Since we are using the row index to refer to position, then the boundary conditions are defined at the start and end rows of the T matrix. So even in your case, it would be the same. The boundary condition at x=0 is set using T[ 0 , : ] (First row). And the boundary condition at x=2 is set using T[ -1 , : ] (Last row).